The equilibrium constant at $298 \ K$ for a reaction $A + B \rightleftharpoons C + D$ is $100$. If the initial concentration of all the four species were $1 \ M$ each,then the equilibrium concentration of $D$ (in $mol \ L^{-1}$) will be:

The partial pressures of an equilibrium mixture of $H_2$,$N_2$,and $NH_3$ are $2 \, atm$,$1 \, atm$,and $3 \, atm$ respectively. If the value of $K_P$ for the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$ at $725 \, K$ is $4.28 \times 10^{-5} \, atm^{-2}$,in which direction will the reaction proceed?

The values of $K_{P_1}$ and $K_{P_2}$ for the reactions
$X \rightleftharpoons Y + Z$ --- $(1)$
$A \rightleftharpoons 2B$ --- $(2)$
are in the ratio of $9 : 1$. If the degree of dissociation of $X$ and $A$ is equal,then the total pressure at equilibrium for $(1)$ and $(2)$ are in the ratio:

Calculate:
$(a)$ $\Delta G^{\circ}$ and
$(b)$ the equilibrium constant for the formation of $NO_2$ from $NO$ and $O_2$ at $298 \, K$
$NO_{(g)} + 1/2 O_{2(g)} \longleftrightarrow NO_{2(g)}$
Given:
$\Delta G^{\circ}_f(NO_2) = 52.0 \, kJ/mol$
$\Delta G^{\circ}_f(NO) = 87.0 \, kJ/mol$
$\Delta G^{\circ}_f(O_2) = 0 \, kJ/mol$

$6.9 \ g$ of $N_2O_4$ is taken in a $0.5 \ L$ closed vessel at $400 \ K$. For the equilibrium $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,the total pressure at equilibrium is $9.15 \ atm$. Calculate $K_c$,$K_p$,and the partial pressure of each component.

For the reaction $SO_{2(g)} + NO_{2(g)} \rightleftharpoons SO_{3(g)} + NO_{(g)}$,the equilibrium constant $K_c$ is $16$. If $1 \ mol$ of each gas is taken in a $1 \ dm^3$ vessel,the equilibrium concentration of $NO$ will be ....